Evidence of fractal structures in hadrons

This study focuses on the presence of (multi)fractal structures in confined hadronic matter through the momentum distributions of mesons produced in proton-proton collisions between 23 GeV and 63 GeV. The analysis demonstrates that the $q$-exponential behaviour of the particle momentum distributions is consistent with fractal characteristics, exhibiting fractal structures in confined hadronic matter with features similar to those observed in the deconfined quark-gluon plasma (QGP) regime. Furthermore, the systematic analysis of meson production in hadronic collisions at energies below 1 TeV suggests that specific fractal parameters are universal, independently of confinement or deconfinement, while others may be influenced by the quark content of the produced meson. These results pave the way for further research exploring the implications of fractal structures on various physical distributions and offer insights into the nature of the phase transition between confined and deconfined regimes.

[1]  Kendrick M. Smith,et al.  Power-law Distribution and Scale-invariant Structure from the First CHIME/FRB Fast Radio Burst Catalog , 2022, Research in Astronomy and Astrophysics.

[2]  A. Deppman,et al.  Nonextensive Statistics in High Energy Collisions , 2022, Physics.

[3]  A. Seryi,et al.  Electron-Hadron Colliders: EIC, LHeC and FCC-eh , 2022, Frontiers in Physics.

[4]  F. Guo,et al.  Selected Science Opportunities for the EicC , 2020, 2008.00102.

[5]  A. Deppman,et al.  Fractals, nonextensive statistics, and QCD , 2019, Physical Review D.

[6]  A. Deppman,et al.  Bag-type model with fractal structure , 2019, Physical Review D.

[7]  J. Cleymans,et al.  On the precise determination of the Tsallis parameters in proton - proton collisions at LHC energies , 2017, 1709.07376.

[8]  A. Deppman,et al.  Quark matter revisited with non-extensive MIT bag model , 2017, The European Physical Journal A.

[9]  Gergely Gábor Barnaföldi,et al.  Systematic Analysis of the Non-Extensive Statistical Approach in High Energy Particle Collisions - Experiment vs. Theory , 2017, Entropy.

[10]  M. G. Echevarria,et al.  Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order , 2016, Journal of High Energy Physics.

[11]  A. Deppman.  Thermodynamics with fractal structure, Tsallis statistics and hadrons , 2016, 1601.02400.

[12]  M. Diehl.  Introduction to GPDs and TMDs , 2015, 1512.01328.

[13]  G. Wilk,et al.  Nonextensive Nambu-Jona-Lasinio Model of QCD matter , 2015, 1510.08516.

[14]  J. Huston,et al.  New parton distribution functions from a global analysis of quantum chromodynamics , 2015, 1506.07443.

[15]  A. Deppman,et al.  Non extensive thermodynamics for hadronic matter with finite chemical potentials , 2015 .

[16]  M. D. Azmi,et al.  Transverse momentum distributions in proton–proton collisions at LHC energies and Tsallis thermodynamics , 2014, 1401.4835.

[17]  M. Boglione,et al.  Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities , 2013, 1312.6261.

[18]  A. Lavagno,et al.  Power-law quantum distributions in protoneutron stars , 2013 .

[19]  O. Teryaev,et al.  Systematic Properties of the Tsallis Distribution: Energy Dependence of Parameters , 2013, 1302.1970.

[20]  A. Deppman,et al.  Nonextensivity of hadronic systems , 2012, 1210.1725.

[21]  F. Zomer,et al.  A Large Hadron Electron Collider at CERN: Report on the Physics and Design Concepts for Machine and Detector , 2012, 1206.2913.

[22]  A. Deppman.  Self-consistency in non-extensive thermodynamics of highly excited hadronic states , 2012, 1205.0455.

[23]  M. Tokarev,et al.  Generalized z-scaling in proton-proton collisions at high energies , 2007 .

[24]  B. Bodmann,et al.  STRANGE MATTER AND STRANGE STARS WITH TSALLIS STATISTICS , 2007 .

[25]  C. Weiss,et al.  SMALL-x PHYSICS: From HERA to LHC and Beyond , 2005, hep-ph/0507286.

[26]  A. Radyushkin,et al.  Unraveling hadron structure with generalized parton distributions , 2005, hep-ph/0504030.

[27]  G. Wilk,et al.  The Imprints of nonextensive statistical mechanics in high-energy collisions , 2000 .

[28]  Skoro,et al.  Z scaling in hadron-hadron collisions at high energies. , 1996, Physical Review D, Particles and fields.

[29]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[30]  J. Jackson,et al.  Production spectra of π±, K±, p± at large angles in proton-proton collisions in the CERN intersecting storage rings , 1975 .

[31]  Steven C. Frautschi,et al.  Principle of Equivalence for all Strongly Interacting Particles within the S-Matrix Framework , 1961 .

[32]  R. Hagedorn,et al.  Statistical thermodynamics of strong interactions at high-energies. 2. Momentum spectra of particles produced in pp-collisions , 1965 .